tautology help

**srk619** · November 17th 2008, 08:28 AM

hi

can anyone help figure this out:

**Jhevon** · November 17th 2008, 08:36 AM

Originally Posted by srk619

hi

can anyone help figure this out:

Use a truth table to find out whether
((A ^ (A => B)) ^ (B => C) ) => C
is a tautology.

here is the (incomplete) truth table. can you finish it? if the last column has T in all its entries, then the statement in question is a tautology

$\begin{array}{|c|c|c|c|c|c|} \hline A & B & C & A \implies B & B \implies C & \{ [(A \wedge (A \implies B)] \wedge (B \implies C) \} \implies C \\ \hline T & T & T & & & \\ \hline T & T & F & & & \\ \hline T & F & T & & & \\ \hline T & F & F & & & \\ \hline F & T & T & & & \\ \hline F & T & F & & & \\ \hline F & F & T & & & \\ \hline F & F & F & & & \\ \hline \end{array}$

**srk619** · November 17th 2008, 09:09 AM

i think i got it

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